Use linear discriminant analysis (LDA) to build a classification rule to classifying the Bumpus bird data into two groups ("survived" and "died") based on the 5 numerical measurements. Assume equal prior probabilities of surviving and dying.

The Bumpus bird data (along with a survival/death indicator vector) can be read in using the following R code:

bumpbird <- read.table("http://people.stat.sc.edu/hitchcock/bumpusbird.txt", header=T)

names(bumpbird) <- c("ID", "tot.length", "alar.length", "beak.head.length", "humerus.length", "keel.stern.length") attach(bumpbird)

bumpbird.numeric <- bumpbird[,-1] bumpbird.IDs <- bumpbird[,1]

survival.indicator <- as.factor(c(rep("survived",times=21),rep("died",length=28)))

(a) Use the LDA rule to predict the survival status for a hypothetical bird with: tot.length=156, alar.length=242, beak.head.length=31.4, humerus.length=18.1, keel.stern.length=19.4 Give the probability of surviving for such a bird.

(b) Find the plug-in misclassification rate and the cross-validation misclassification rate for the LDA classification rule.